Abstract Hierarchical Implicit Surface Refinement

A novel method of hierarchical implicit modeling is presented, in which an implicit object is modeled by using a hierarchy of implicit surfaces. The hierarchy provides both layered local refinement and global deformation. Local refinement allows the introduction of higher-level detailed surfaces. Global deformation changes the overall shape of the surface while maintaining the integrity of surface details. The model is gradually refined by introducing appropriate new primitives in the specified surface areas. Refinement constraints, such as local surface area and level of the surface (within the hierarchy) are designed to be applied to the implicit object so as to achieve finer control over the local surface. The method provides a dynamic representation of implicit surfaces and can be used not only in modeling complex implicit objects, but also in animating the surfaces and simulating the deformations of various objects